Residual quantum symmetries of the Restricted sine-Gordon theories

Abstract

Various aspects of the Restricted sine-Gordon (RSG) theories for the coupling β 2 8π = p p+1 are examined. The particle spectrum is interpreted in terms of generalized kinks for the RSG potential, which is shown to effectively contain p−1 degenerate vacua. Simple arguments based on a study of the topological charge show that in the massless limit the RSG theories reduce to the Feigin-Fuchs construction. We find that the RSG S-matrices are characterized by a symmetry which generalizes supersymmetry to a fractional supersymmetry, and that the particles have fractional spin and statistics. In accordance with these results, we find some non-local chiral algebras in the minimal models that generalize the superconformal algebra, and whose currents are conserved in perturbation theory.